Star Trek Continues: a fan-made continuation of the original Star Trek series.
While it is a bit weird at first to see those characters played by different actors, those are actually as good, production-wise, as the originals, if not better (a few touches of modern CGI where needed also helps).
Being made fifty years later, it is more sombre, even sometimes tragic, and with a more emotional focus. However, it still is the old Star Trek we know and love, and its more modern style is probably better for today's audiences. Honestly, I think it may be the best show to introduce Star Trek to someone so far.
And for some reason, no-one told me about it since a month ago. grumble in a corner
(Yes, it is the same actor in the first episode here than in the original episode)